If you terminate employment, your E-2 visa, issued for work with one employer, is null and void. To work at another institution, you generally must get a Letter of Release from the current employer. Then, getting an E-2 for a new employer requires all new paperwork (signed contract, diploma, transcripts, photos, CV, etc.) and leaving the country to obtain the E-2 from an Korean embassy abroad.

If you are unhappy with your job, look for another job, explain why y ou are seeking new employment. It is my understanding that your new employer can ask your current employer to transfer the contract. If it is a private school, they might just do this for a fee.

Just ask the new potential employer. A potenital employer will most likely assume the cost of you transfering the contract visa or pay for most of your transportation costs if you do have to leave the country.